Fast and High Accurate Algorithm and Its Implementation for Acoustic waves and Elastic Waves in Reverse Time Migration

逆时偏移技术（Reversetimemigration，RTM）主要应用于解决地震成像问题，是现行偏移方法中最精确的一种。逆时偏移成像的优势在于其成像过程是基于数值方法求解双程波动方程，不仅没有角度限制，还充分考虑了回转波、棱柱波、多次反射等复杂传播路径，因此能够在高倾角、速度变化剧烈的复杂地下结构中得到高质量的图像。逆时偏移成像质量优于基于射线理论的Kirchhoff偏移或基于单程波动方程的其他偏移方法，然而求解双程波动方程计算量大、计算需要的存储资源多，导致逆时偏移成像计算成本较高，这在一定程度上限制了其在工业应用中的推广。 缓解计算瓶颈可以从两个方面入手：一方面使用快速、高精度算法求解...Reverse time migration (RTM) is a high-efficiency tools for seismic imaging. RTM has been considered to be one of the most accurate seismic pre-stack depth migration methods, especially for imaging geologically complex structures. RTM calculates the two-way wave equations numerically. It has no angle limit, and has considered complex propagating paths, such as turning, prismatic and multiple refle...学位：理学博士院系专业：物理科学与技术学院_无线电物理学号：1982011015405

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal